US 6356666 B1 Abstract On the image compression side, each lossless wavelet transformation coefficient on which a lossless wavelet transformation for an image is effected, is first subjected to quantization and entropy coding in a coarse step size. Thereafter, quantization error signals are successively subjected to quantization and entropy coding in a fine step size to thereby generate a progressive coded bit stream. On the image expansion side, lossless wavelet transformation coefficients obtained by entropy decoding and inverse quantization are subjected to inverse lossless wavelet transformations every coded bit streams bearing respective stages for image progressive reconstruction display. Data obtained by the inverse transformations is added to the already-reconstructed image data together with updated auxiliary information about each image to thereby reconstruct and display the image progressively. Now, the updated auxiliary information necessary to update the image is generated from some of information about lossless wavelet transformation coefficients necessary to update the image quality by one stage and some of lossless wavelet transformation coefficients necessary to generate the already-displayed image, whereby it is not necessary to hold all the information about lossless wavelet transformation coefficients necessary to generate a pre-updating image and memory's capacity can be reduced.
Claims(21) 1. An image compressing/expanding method, comprising:
on the image compression side, performing quantization and entropy coding on a lossless wavelet transformation coefficient subjected to a lossless wavelet transformation; and
on the image expansion side, adding pre-inverse-transformation data, which includes a lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization, to the coefficient-domain update data subjected to entropy decoding and inverse quantization, and thereafter performing said inverse lossless wavelet transformation on the result of addition to thereby generate an image.
2. An image compressing/expanding method comprising:
on the image compression side, performing quantization and entropy coding on each lossless wavelet transformation coefficient subjected a lossless wavelet transformation; and
on the image expansion side, effecting an inverse lossless wavelet transformation on a lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization to thereby generate an image, and generating image-domain update information necessary upon updating an image by adding the image generated by the inverse lossless wavelet transformation to the already generated image, from information necessary upon updating the quality of the image by a next stage and some of information about each transformation coefficient immediately before the execution of said inverse lossless wavelet transformation.
3. An image compressing/expanding device, comprising:
an image compressing device including,
a lossless wavelet transformation unit for subjecting a digital image to a lossless wavelet transformation; and
a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformation to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and simultaneously generating a progressive coded bit stream while repeating this operation until the value of a quantization error reaches zero; and
an image expanding device including,
an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N types of data necessary to update data of said progressive coded bit stream by N stages as one processing unit, thereby generating an image;
a transformation coefficient buffer for holding some of pre-inverse-transformation coefficient data generated upon the generation of the image; and
a transformation coefficient information updater for adding image-domain update information generated from data obtained by subjecting transformation coefficient data obtained by effecting entropy decoding and inverse quantization on the next processing unit bearing information for updating said image to an inverse lossless wavelet transformation with said inverse lossless wavelet transformation unit, some of the same inversely-transformed data and the data held in said transformation coefficient buffer, to the immediately preceding reconstructed/displayed image in an image domain, thereby to update image information.
4. The image compressing/expanding device according to
5. The image compressing/expanding device according to
6. The image compressing/expanding device according to
7. The image compressing/expanding device according to
8. An image compressing/expanding device, comprising:
an image compressing device including,
a lossless wavelet transformation unit for subjecting a digital image to a lossless wavelet transformation; and
a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformations to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and simultaneously generating a progressive coded bit stream while repeating this operation until the value of a quantization error reaches zero; and
an image expanding device including,
an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N types of data necessary to update data of the progressive coded bit stream by N stages as one processing unit, thereby generating an image;
a transformation coefficient buffer for holding information necessary upon updating the quality of the image by a further stage, of the lossless wavelet transformation coefficients; and
an image-domain update information generator for generating image-domain update information additionally necessary upon updating the image by adding the image generated by the inverse lossless wavelet transformation to the already-reconstructed image from the information stored in said transformation coefficient buffer and information about each transformation coefficient immediately before the execution of the inverse lossless wavelet transformation.
9. The image compressing/expanding device according to
an image compressing device having at least one S transformation part for implementing a lossless wavelet transformation by an S transformation; and
an image expanding device having at least on Inverse S transformation part for implementing an inverse lossless wavelet transformation by an inverse S transformation, and wherein the image-domain update information is generated only from LSB of respective lossless wavelet S transformation coefficients necessary to generate a pre-updating image through a lossless wavelet inverse S transformation and LSB of lossless wavelet S transformation coefficients bearing only information necessary for updating.
10. The image compressing/expanding device according to
an image compressing device having at least on TS transformation part for implementing a lossless wavelet transformation by a TS transformation, and
an image expanding device having at least one inverse TS transformation part for implementing an inverse lossless wavelet transformation by an inverse TS transformation, and wherein the generation of image-domain update information under a progressive reconstructing process through an inverse transformation set in a stage preceding an inverse S transformation is performed as a first stage based only on the two rightmost bits of respective transformation coefficients necessary to generate pre-updating data through the same inverse transformation and the two rightmost bits of respective transformation coefficients bearing only information newly necessary for updating, and as a second stage, the so-obtained update information is progressively reconstructed through the inverse S transformation as an input, whereby the progressive reconstruction display of an image at the image expanding device is performed in accordance with the two-stage processing through the inverse S transformation.
11. An image compressing/expanding device according to
12. An image compressing/expanding device, comprising:
an image compressing device including,
a lossless wavelet transformation unit for subjecting a digital image to a lossless wavelet transformation; and
a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformations to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and simultaneously generating a progressive coded bit stream while repeating this operation until the value of a quantization error reaches zero; and
an image expanding device including,
an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N stages of data necessary to update data of said progressive coded bit stream by N stages as one processing unit, thereby generating an image;
a transformation coefficient buffer for holding information necessary upon updating the quality of the image by a further stage, of the lossless wavelet transformation coefficients;
an image-domain update information generator for generating image-domain update information additionally necessary upon updating the image by adding the image generated by the inverse lossless wavelet transformation to the already-reconstructed image from the information stored in said transformation coefficient buffer and information about each transformation coefficient immediately before the execution of the inverse lossless wavelet transformation;
a zero coefficient determinator for determining, immediately before the execution of the inverse lossless wavelet transformation, whether the values of the respective transformation coefficients are zero; and
a zero coefficient arithmetic omitter for omitting a sum-of-products arithmetic operation for an inverse lossless wavelet transformation effected on the transformation coefficients whose values are zero.
13. The image compressing/expanding device according to
14. An image compressing device, comprising:
an image compressing device including,
a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformation to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and repeating this operation until the value of a quantization error reaches zero.
15. The image compressing device according to
at least one S transformation part for implementing a lossless wavelet transformation by an S transformation.
16. The image compressing device according to
at least on TS transformation part for implementing a lossless wavelet transformation by a TS transformation.
17. The image compressing device according to
an S transformation/TS transformation selector for repeatedly applying sub-band decomposition to the lowest frequency sub-band components generated by the lossless wavelet transformation every x and y directions so as to decompose into a desire number of sub-bands and selecting the corresponding lossless wavelet transformation so as to selectively use the S and TS transformations according to the respective directions and respective repetitions without always having to use a single transformation.
18. An image expanding device comprising:
an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N types of data necessary to update data of the progressive coded bit stream by N stages as one processing unit, thereby generating an image;
a transformation coefficient buffer for holding information necessary upon updating the quality of the image by a further stage, of the lossless wavelet transformation coefficients; and
an image-domain update information generator for generating image-domain update information additionally necessary upon updating the image by adding the image generated by the inverse lossless wavelet transformation to the already-reconstructed image, from the information stored in said transformation coefficient buffer and information about each transformation coefficient immediately before the execution of the inverse lossless wavelet transformation.
19. The image expanding device of
at least on Inverse S transformation part for implementing an inverse lossless wavelet transformation by an inverse S transformation, and wherein the image-domain update information is generated only from LSB of respective lossless wavelet S transformation coefficients necessary to generate a pre-updating image through a lossless wavelet inverse S transformation and LSB of lossless wavelet S transformation coefficients bearing only information necessary for updating.
20. The image expanding device of
at least one inverse TS transformation part for implementing an inverse lossless wavelet transformation by an inverse TS transformation, and wherein the generation of image-domain update information under a progressive reconstructing process through an inverse transformation set in a stage preceding an inverse S transformation is performed as a first stage based only on the two rightmost bits of respective transformation coefficients necessary to generate pre-updating data through the same inverse transformation and the two rightmost bits of respective transformation coefficients bearing only information newly necessary for updating, and as a second stage, the so-obtained update information is progressively reconstructed through the inverse S transformation as an input, whereby the progressive reconstruction display of an image at the image expanding device is performed in accordance with the two-stage processing through the inverse S transformation.
21. An image compressing/expanding method comprising:
on the image compression side, performing quantization and coding on transformed image data to generate a coded bit stream that is added to a previously generated coded bit stream to generate a progressive coded bit stream and repeating this operation N times until the value of a quantization error reaches zero;
on the image expansion side, performing decoding, inverse quantization, and inverse transformation on data of the progressive coded bit stream necessary to update the progressive coded bit stream by N stages, thereby generating an image.
Description This application is the national phase under 35 U.S.C. §371 of prior PCT International Application No. PCT/JP97/02655 which has an International filing date of Jul. 30, 1997 which designated the United States of America. This invention relates to a method of and a device for performing image compression (image coding) and image expansion (image decoding), which are based on lossless wavelet transformations on which attention is focused as a platform of the next-generation image coding system capable of implementing a unified form of lossless coding/lossy coding. In an image compressing/expanding device constructed based on conventional linear transformations such as a wavelet transformation, DCT, etc., the implementation of the function of progressively reproducing and displaying image data by fewer numbers of execution memories and fewer numbers of arithmetic operations takes advantage of the fact that an inverse wavelet transformation, a DCT inverse transformation or the like is a linear transformation (linear system). Further, since the arithmetic order of operations necessary for the inverse transformation and addition made upon updating information in a transformation coefficient domain is changeable, the order of these is changed, an inverse transformation is effected only on transformation coefficient information necessary for information updating and the so-obtained result is added to the immediately-preceding reconstructed image data in an image domain, whereby the progressive reconstruction display of the image has been realized. FIG. 1 is a block diagram of an image expanding device which executes a processing order obtained from the changing of the arithmetic order created based on the contents described in, for example, IEEE Data Compression Conference (DCC-96), April 1996 “Fast Reconstruction of Subband Decomposed Signals for Progressive Transmission”. In the drawing, pre-updating transformation coefficient information b In the progressive reconstruction display of the image by the image compressing/expanding device based on the conventional linear transformations as described above, the inverse transformation is effected only on the transformation coefficient information necessary for information updating by using the linearity of the transformation. The so-obtained result is added to the immediately preceding reconstructed image. Thus, the progressive reconstruction display of the image can be implemented without additionally holding information about transformation coefficients used to reconstruct the immediately preceding reconstructed image. As a result, execution memories could be reduced in number. Further, the speeding up of processing can be implemented by utilizing a property of the coefficients whose values are zero, increase the number and omitting inverse transformation arithmetic operations on these coefficients when data is reconstructed only from the transformation coefficients necessary for updating. However, an image compressing/expanding device based on conventional linear transformations has the problem in that a high picture-quality reconstructed image having the image quality of strictly the same level as the original image cannot be obtained due to a quantization error or the like. While the image compressing/expanding device based on the lossless wavelet transformation can obtain the high picture-quality reconstructed image, the inverse lossless wavelet transformation used as the platform of the image expanding device includes a non-linear arithmetic operation. Therefore, the progressive reconstruction display of the image must be inevitably implemented by updating information in a wavelet transformation coefficient domain and thereafter performing an inverse lossless wavelet transformation on it in order to implement the progressive reconstruction display of the image. Thus, the lossless wavelet transformation coefficients used to generate the pre-updating image, i.e., all the information immediately before the execution of the inverse lossless wavelet transformation must be held to update the displayed image. Therefore, a problem arises in that the size of the execution memory is reduced and a high-speed image progressive reconstruction display cannot be implemented. Further, a problem arises in that since the number of transformation coefficients zero in value relatively increases if an inverse lossless wavelet transformation is effected on wavelet transformation coefficients comprised of only information necessary for updating, it is quite natural that the number of arithmetic operations at the inverse lossless wavelet transformation can be reduced and the processing can be speeded up by using its relative increase, but the number of the transformation coefficients zero in value relatively decreases because the inverse lossless wavelet transformation is made after the updating of information in a transformation coefficient domain. Thus the speeding up of the processing utilizing the property that many coefficients zero in value are included in the wavelet transformation coefficients indicative of the information necessary for updating cannot be expected. Namely, the image compressing/expanding device based on the linear transformation and the image compressing/expanding device based on the lossless wavelet transformation have both merits and demerits respectively. With the foregoing problems in view, it is therefore an object of the present invention to provide an image compressing/expanding device based on a lossless wavelet transformation/inverse transformation, which is capable of implementing a progressive reconstruction display of an image while limiting or controlling the consumption of execution memories, thereby obtaining a high picture-quality reconstructed image. An image compressing/expanding method according to the invention as claimed in claim 1 comprises, on the image compression side, performing quantization and entropy coding on a lossless wavelet transformation coefficient subjected to a lossless wavelet transformation, and on the image expansion side, adding pre-quantization data generated when an inverse lossless wavelet transformation is effected on a lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization to thereby generate an image, to the next updated data subjected to entropy decoding and inverse quantization, and thereafter performing the inverse lossless wavelet transformation on the result of addition. Owing to such a construction, the image compressing/expanding method based on the lossless wavelet transformation brings about an effect in that a progressive representation can be implemented and a high picture-quality reconstructed image having image quality of strictly the same level as the original image can be obtained. An image compressing/expanding method according to the invention as claimed in claim 2 comprises, on the image compression side, performing quantization and entropy coding on each lossless wavelet transformation coefficient subjected a lossless wavelet transformation, and on the image expansion side, effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization to thereby generate an image, and generating updated auxiliary information necessary upon updating an image by adding the image generated by the inverse lossless wavelet transformation to the already generated image, from information necessary upon updating the quality of the image by one stage and some of information about each transformation coefficient immediately before the execution of the inverse lossless wavelet transformation. Owing to such a construction, an effect is brought about in that upon implementation of a progressive reconstruction display, it is unnecessary to hold all the transformation coefficient information used to generate a pre-updating image and an execution memory can be reduced in size. An image compressing/expanding device according to the invention as claimed in claim 3 comprises an image compressing device including a lossless wavelet transformation unit for subjecting a digital image to a lossless wavelet transformation, and a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformations to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and simultaneously generating a progressive coded bit stream while repeating this operation until the value of a quantization error reaches zero, and an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N types of data necessary to update data of the progressive coded bit stream by N stages as one processing unit, thereby generating an image, a transformation coefficient buffer for holding some of pre-quantization transformation coefficient data generated upon the generation of the image, and a transformation coefficient information updater for adding updated auxiliary information generated from data obtained by subjecting transformation coefficient data obtained by effecting entropy decoding and inverse quantization on the next processing unit bearing information for updating the image on an inverse lossless wavelet transformation with the inverse lossless wavelet transformation unit, some of the same inversely-transformed data and the data held in the transformation coefficient buffer, to the immediately preceding reconstructed/displayed image in an image domain, thereby to update image information. Owing to such a construction, the image compressing/expanding method based on the lossless wavelet transformation allows a progressive representation to be implemented and a high picture-quality reconstructed image having image quality of strictly the same level as the original image can be obtained. An image compressing/expanding device according to the invention as claimed in claim 4 comprises an image compressing device including a lossless wavelet transformation unit for subjecting a digital image to a lossless wavelet transformation, and a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformations to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and simultaneously generating a progressive coded bit stream while repeating this operation until the value of a quantization error reaches zero, and an image expanding device including an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N types of data necessary to update data of the progressive coded bit stream by N stages as one processing unit, thereby generating an image, a transformation coefficient buffer for holding information necessary upon updating the quality of the image by a further stage, of the lossless wavelet transformation coefficients, and an updated auxiliary information generator for generating updated auxiliary information additionally necessary upon updating the image by adding the image generated by the inverse lossless wavelet transformation to the already-reconstructed image from the information stored in the transformation coefficient buffer and information about each transformation coefficient immediately before the execution of the inverse lossless wavelet transformation. Owing to such a construction, an effect is brought about in that upon implementation of a progressive reconstruction display, it is unnecessary to hold all the transformation coefficient information used to generate a pre-updating image and an execution memory can be reduced in size. An image compressing/expanding device according to the invention as claimed in claim 5 comprises an image compressing device having at least one S transformation part for implementing a lossless wavelet transformation by an S transformation, and an image expanding device having at least one Inverse S transformation part for implementing an inverse lossless wavelet transformation by an inverse S transformation, and wherein the updated auxiliary information is generated only from LSB of respective lossless wavelet S transformation coefficients necessary to generate a pre-updating image through a lossless wavelet inverse S transformation and LSB of lossless wavelet S transformation coefficients bearing only information necessary for updating. Owing to such a construction, an effect is brought about in that the amount of information about transformation coefficients held to generate updated auxiliary information necessary to implement a progressive reconstruction display can be limited to one bit for each transformation coefficient and the size of an execution memory can be reduced. An image compressing/expanding device according to the invention as claimed in claim 6 comprises an image compressing device having at least one TS transformation part for implementing a lossless wavelet transformation by a TS transformation, and an image expanding device having at least one inverse TS transformation part (constructed by an S transformation and a linear transformation and a non-linear transformation placed in its previous stage) for implementing an inverse lossless wavelet transformation by an inverse TS transformation, and wherein the generation of updated auxiliary information under a progressive reproducing process through an inverse transformation set in a stage preceding an inverse S transformation is performed as a first stage based only on the two rightmost bits of respective transformation coefficients necessary to generate pre-updating data through the same inverse transformation and the two rightmost bits of respective transformation coefficients bearing only information newly necessary for updating, and as a second stage, the so-obtained updated information is progressively reconstructed through the inverse S transformation as an input, whereby the progressive reconstruction display of an image at the image expanding device is performed in accordance with the two-stage processing through the inverse S transformation. Owing to such a construction, an effect is brought about in that as compared with the case where the S transformation and Inverse S transformation are used, a higher picture-quality reconstructed image can be obtained if compared at the same bit rate. An image compressing/expanding device according to the invention as claimed in claim 7, is constructed in such a manner that the image compressing device or the image expanding device is provided with an S transformation/TS transformation selector for repeatedly applying band division to the lowest frequency components generated by the lossless wavelet transformation every x and y directions so as to divide into a desired number of bands and selecting the corresponding lossless wavelet transformation so as to selectively use the S and TS transformations according to the respective directions and respective repetitions without always having to use a single transformation. Owing to such a construction, an effect is brought about in that as compared with the case in which the S transformation and Inverse S transformation are used, a higher picture-quality reconstructed image can be obtained if compared at the same bit rate, and the size of an execution memory can be reduced as compared with the case in which a TS transformation and an inverse TS transformation are used as all the transformations and inverse transformations. An image compressing/expanding device according to the invention as claimed in claim 8 comprises an image compressing device including a lossless wavelet transformation unit for subjecting a digital image to a lossless wavelet transformation, and a progressive coding generation unit for subjecting lossless wavelet transformation coefficients obtained as a result of lossless wavelet transformations to quantization and entropy coding to thereby generate a coded bit stream added to an already generated coded bit stream and simultaneously generating a progressive coded bit stream while repeating this operation until the value of a quantization error reaches zero, and an image expanding device including an inverse lossless wavelet transformation unit for effecting an inverse lossless wavelet transformation on each lossless wavelet transformation coefficient subjected to entropy decoding and inverse quantization with each of N types of data necessary to update data of the progressive coded bit stream by N stages as one processing unit, thereby generating an image, a transformation coefficient buffer for holding information necessary upon updating the quality of the image by a further stage, of the lossless wavelet transformation coefficients, an updated auxiliary information generator for generating updated auxiliary information additionally necessary upon updating the image by adding the image generated by the inverse lossless wavelet transformation to the already-reconstructed image from the information stored in the transformation coefficient buffer and information about each transformation coefficient immediately before the execution of the inverse lossless wavelet transformation, a zero coefficient determinator for determining, immediately before the execution of the inverse lossless wavelet transformation, whether the values of the respective transformation coefficients are zero, and a zero coefficient arithmetic omitter for omitting a sum-of-products arithmetic operation for an inverse lossless wavelet transformation effected on the transformation coefficients whose values are zero. Owing to such a construction, an effect is brought about in that a progressive reconstruction display process can be speeded up. An image compressing/expanding device according to the invention as claimed in claim 9 is constructed such that the image expanding device is provided with a zero number counter for counting the number (zero number) of continuously-generated values zero of the transformation coefficients and outputting a signal used to omit the sum-of-products arithmetic operation for the inverse lossless wavelet transformation when the number thereof reaches a predetermined counted value. Owing to such a construction, an effect is brought about in that a progressive reconstruction display process can be further speeded up. An image compressing/expanding device according to the invention as claimed in claim 10 is constructed such that the image compressing/expanding device as claimed in any of claims 3 to 9 is applied to an image decoding process of a facsimile. Owing to this construction, an effect is brought about in that upon the image decoding process of the facsimile, the consumption of execution memories can be reduced and a high picture-quality image can be obtained. An image compressing/expanding device according to the invention as claimed in claim 11 is constructed such that the image compressing/expanding device as claimed in any of claims 3 to 9 is applied to an image decoding process of a portable information terminal. Owing to this construction, an effect is brought about in that upon the image decoding process of the portable terminal, the consumption of execution memories can be reduced and a high picture-quality image can be obtained. An image compressing/expanding device according to the invention as claimed in claim 12 is construction such that the image compressing/expanding device as claimed in any of claims 3 to 9 is applied to an image decoding process of a high image-quality display unit. Owing to this construction, an effect is brought about in that upon the image decoding process of the high image-quality display unit, the consumption of execution memories can be reduced and a high picture-quality image can be obtained. An image compressing/expanding device according to the invention as claimed in claim 13 is constructed such that the image compressing/expanding device as claimed in any of claims 3 to 9 is applied to an image decoding process of a printer. Owing to this construction, an effect is brought about in that upon the image decoding process of the printer, the consumption of execution memories can be reduced and a high picture-quality image can be obtained. FIG. 1 is block diagram showing a configuration of a conventional image expanding device; FIG. 2 is a block diagram illustrating a configuration of an image compressing device according to an embodiment 1 of the present invention; FIG. 3 is a block diagram depicting a configuration of an image expanding device according to an embodiment 1 of the present invention; FIG. 4 is a block diagram showing a configuration of an image expanding device according to an embodiment 2 of the present invention; FIG. 5 is a block diagram illustrating configurations of a lossless wavelet transformation unit and an inverse lossless wavelet transformation unit of an image compressing/expanding device according to an embodiment 3 of the present invention; FIG. 6 is a block diagram showing a configuration of an S transformation part employed in the embodiment 3 of the present invention; FIG. 7 is a block diagram illustrating a configuration of a lossless wavelet transformation unit and an inverse lossless wavelet transformation unit of an image compressing/expanding device according to an embodiment 4 of the present invention; FIG. 8 is a block diagram depicting the details of a configuration of an inverse TS transformation part employed in the embodiment 4 of the present invention; FIG. 9 is a block diagram showing a configuration of a transformation unit (hereinafter called “T transformer”) constructed by a linear transformation and a nonlinear transformation placed in a stage prior to an S transformation employed in the embodiment 4 of the present invention; FIG. 10 is a diagram showing a table for generating updated auxiliary information; FIG. 11 is a block diagram illustrating configurations of a lossless wavelet transformation unit and an inverse lossless wavelet transformation unit of an image compressing/expanding device according to an embodiment 5 of the present invention; and FIG. 12 is a block diagram depicting a configuration of an image expanding device according to an embodiment 6 of the present invention. Best modes for carrying out the invention will hereinafter be explained in accordance with the accompanying drawings to describe this invention in more details. Embodiment 1 FIG. 2 is a block diagram showing a configuration of an image compressing device according to an embodiment 1 of the present invention. In the drawing, reference numeral FIG. 3 is a block diagram illustrating a configuration of an image expanding device according to an embodiment 1 of the present invention. In the drawing, reference numeral The inverse lossless wavelet transformation unit Since the first and second y-direction one-dimensional inverse lossless wavelet transformation parts The operation will next be described. With respect to an image inputted to the image compressing device, an image frequency band thereof is decomposed into frequency sub-bands by the x-direction one-dimensional lossless wavelet transformer Next, the reconstructed lossless wavelet transformation coefficients are sent to the progressive coded data generation unit In order to additionally encode quantized errors reconstructed in the quantizer The encoded data obtained by the entropy encoding with the entropy encoder Further, in order to encode information impaired by the quantization of the so-updated image data, the local inverse quantization controller In the above-described processing block, the progressive coding controller In the image expanding device illustrated in the embodiment 1, as shown in FIG. 3, when the progressive coded bit stream is inputted to the entropy decoder Since, in this case, the y-direction and x-direction one-dimensional inverse lossless wavelet transformation parts At this time, data b Even in this case, the data prior to being subjected to the inverse lossless wavelet transformation is held in the transformation coefficient buffer According to the embodiment 1 as described above, an effect is brought about in that each lossless wavelet transformation coefficient necessary to produce the image immediately before its updating is held, the value of the same transformation coefficient and the value obtained by entropy-decoding and reverse-quantizing the coded data stream necessary for updating are added together within a transformation coefficient domain, followed by execution of the inverse lossless wavelet transformation, whereby a progressive representation can be realized by the image compressing/expanding device based on the lossless wavelet transformation, thereby making it possible to obtain a high picture-quality reconstructed image which finally results in the same image as the original image. Embodiment 2 FIG. 4 is a block diagram showing a configuration of an image expanding device according to an embodiment 2 of the present invention. The same parts as those shown in FIG. 3 are identified by like reference numerals and the description of certain common parts will therefore be omitted. In the drawing, an inverse lossless wavelet transformation unit Since the first and second y-direction one-dimensional inverse lossless wavelet transformation parts The operation will next be described. In the image compressing device as shown in FIG. 2 in the first place, the x-direction one-dimensional lossless wavelet transformer Next, the reconstructed lossless wavelet transformation coefficients are sent to the progressive coded data generation unit In order to additionally encode quantized errors reconstructed in the quantizer The encoded data obtained by the entropy encoding with the entropy encoder Further, in order to encode information impaired by the quantization of the so-updated image data, the local inverse quantization controller In the above-described processing block, the progressive coding controller In the image expanding device illustrated in the embodiment 2, as shown in FIG. 4, a progressive decoding processor The first y-direction one-dimensional inverse lossless wavelet transformation part Upon generation of the coarsest image, the data obtained by the inverse quantization of the inverse quantizer Such image updating process is performed in accordance with the control of a progressive coding controller The progressive coding controller Simultaneously, the updated auxiliary information generator Thus, the data necessary to generate finer images out of the encoded data necessary to successively generate the coarse to finer images from the data necessary to generate the coarse images down are successively subjected to an expanding process. Each expanded data obtained in this way is added to the already displayed image data in the image domain, whereby progressive decoding/reconstruction of image coded data subjected to progressive coding, the updating of progressive image data and a progressive image representation are implemented. In the lossless wavelet transformation unit While the processing performed in the order of the x-direction one-dimensional dimensional lossless wavelet and the y-direction one-dimensional lossless wavelet is shown in FIG. 2 as one example, the processing of the order of the y-direction one-dimensional lossless wavelet and the x-direction one-dimensional lossless wavelet may be performed. The inverse lossless wavelet transformation unit According to the embodiment 2 as described above, the image progressive reconstruction display is realized by subjecting only the information necessary for updating to the inverse lossless wavelet transformation without performing the inverse lossless wavelet transformation on the information after the updating of the information in the lossless wavelet transformation coefficient domain, and adding the data obtained by the inverse transformation to the pre-updating image together with slight additional information in the image domain. Therefore, an effect is brought about in that it is unnecessary to hold all the transformation coefficient information used to generate the pre-updating image upon implementation of the progressive reconstruction display and the size of an execution memory can be reduced. Further, the progressive reconstruction display is implemented by subjecting only information necessary for updating to the inverse lossless wavelet transformation without performing the lossless wavelet transformation on the information necessary for updating after the information is added to each transformation coefficient used to generate the pre-updating image in the transformation coefficient domain, and adding these in the image domain. As a result, an effect is brought about in that a sum-of-products operation in the inverse lossless wavelet transformation using the fact that the transformation coefficient information necessary for updating contains many zero coefficients, can be omitted so that a progressive reconstruction display process can be speeded up. Embodiment 3 FIG. 5 is a block diagram showing configurations of a lossless wavelet transformation unit Since the first and second y-direction one-dimensional inverse lossless wavelet S transformers The operation of one one-dimensional inverse lossless wavelet S transformer will next be explained with reference to FIG. In the image compressing device using the S transformation, transformation coefficient data (b Now, information about LSB of the transformation coefficient d Subsequent to this, transformation coefficient data (low-frequency component Δs The image x Thus, in the image expanding device according to the embodiment 3, the processing for updating the information in the image domain from the image data obtained by independently inversely S-transforming the encoded data necessary to update the image and the updated auxiliary information α obtained using some of the transformation coefficients used to generate the already-displayed image is repeatedly executed until the encoded data necessary for updating is brought to nothing, whereby the image is progressively reconstructed and displayed from the progressive encoded data by using the S transformation. Thus, the same image as an image prior to being encoded is finally played back and displayed. According to the embodiment 3 as described above, the lossless wavelet transformation in the image compressing device is performed by the S transformation and the inverse lossless wavelet transformation in the image expanding device is carried out by the inverse S transformation, whereby the lossless wavelet transformation and inverse transformation can be implemented by a lower number of arithmetic operations and the amount of information about each transformation coefficient to be held to generate the updated auxiliary information a necessary to implement the progressive reconstruction and representation or display can be limited to one bit per each transformation coefficient. Namely, an effect is brought about in that an execution memory can be reduced. Embodiment 4 FIG. 7 is a block diagram showing configurations of a lossless wavelet transformation unit The first and second y-direction one-dimensional inverse lossless wavelet TS transformers As a result of this construction, a progressive reconstruction display of an image by the image expanding device according to the embodiment 4 can be realized by utilizing progressive reconstruction made through the linear inverse transformer The operation will next be described. If the amount of information necessary to reconstruct the coarsest image is represented as b First, the coarsest image x With respect to the image x The image x Incidentally, fk (wherein k=0, . . . N−1) indicates the result obtained by performing a linear inverse transformation on sk with the linear inverse transformer The progressive reconstruction display of the image through the inverse TS transformations in the image expanding device illustrated in the embodiment 4 will be explained below by reference to a procedure for progressive reconstruction by the linear inverse transformer The inverse T transformer The two rightmost bits of fk−1 corresponding to one of information necessary to generate the updated auxiliary information are obtained if the two rightmost bits of f Similarly, the two rightmost bits of fk are obtained by adding the two rightmost bits of Δfk−1 to the values of the two rightmost bits of fk−1 held and calculating the remainder obtained by dividing the result of addition by 4 in the updated auxiliary data buffer According to the embodiment 4 as described above, the lossless wavelet transformation of the image compressing device is performed based on the TS transformations, whereas the inverse lossless wavelet transformation of the image expanding device is performed based on the inverse TS transformations, whereby an effect is brought about in that as compared with the use of the S transformation and Inverse S transformation, a higher picture-quality reconstructed image can be obtained when compared under the same bit rate. Embodiment 5 In the image compressing/expanding device according to the embodiment 3, the S transformation and Inverse S transformation have always been used as the lossless wavelet transformation and the inverse lossless wavelet transformation, whereas in the image compressing/expanding device according to the embodiment 4, the TS transformations and the inverse TS transformations have always been used as them. On the other hand, in the image compressing/expanding device illustrated in the embodiment 5, respective one-dimensional lossless wavelet transformations may be performed based on the S transformation or TS transformations in the compressing device. Even in the case of the expanding device, the corresponding inverse transformation may be merely carried out in the order opposite to that for the transformations done by the compressing device. Respective one-dimensional inverse lossless wavelet transformations may be performed based on an inverse S transformation or inverse TS transformations. Thus, the embodiment 5 is constructed as shown in FIG. At this time, the S transformation/TS transformation selector The holding of selected information about the S transformation/TS transformations executed upon lossless wavelet transformations to be performed once per x and y directions, besides, upon respective transformations is repeatedly effected on the lowest frequency component next previously obtained by the lossless wavelet transformations to be performed once per x and y directions, by the predetermined number of times in accordance with the control of a sub-band decomposition controller In the image expanding device According to the embodiment 5 as described above, the lossless wavelet transformation of the image compressing device is carried out by a combination of the S transformation and TS transformations, whereas the inverse lossless wavelet transformation of the image expanding device is performed by a combination of the inverse S transformation and inverse TS transformations. Thus, an effect is brought about in that as compared with the case where the progressive reconstruction display of the image is done by the S transformation and Inverse S transformation alone, higher image quality is obtained if compared at the same bit rate, and as compared with the case in which the progressive reconstruction display of the image is performed by the TS transformations and inverse TS transformations alone, less updated auxiliary information is provided, i.e., the capacity of an execution memory is reduced, whereby the progressive reconstruction display can be performed. Embodiment 6 FIG. 12 is a block diagram showing a configuration of an image expanding device in an image compressing/expanding device according to an embodiment 6 of the present invention. The same parts as those employed in the embodiment 2 shown in FIG. 4 are identified by the same reference numerals and the description of certain common parts will therefore be omitted. In the drawing, reference numeral The first and second y-direction one-dimensional inverse lossless wavelet transformation parts According to the embodiment 6, the omission of arithmetic operation of the inverse lossless wavelet transformation on each transformation coefficient zero in value is implemented to execute the image progressive reconstruction display at high speed. Namely, the zero coefficient determinator When the lossless wavelet transformation coefficient takes the value of zero continuously, the zero counter Embodiment 7 The image compressing/expanding devices according to the aforementioned respective embodiments are applied to a facsimile, a portable terminal, a display unit or a printer so as to perform an image decoding process, thereby making it possible to obtain an image high in picture quality. Incidentally, the S transformation, inverse S transformation, TS transformation and inverse TS transformation in the aforementioned embodiments 3 through 5 are respectively represented by the following arithmetic expressions: S transformation (forward transformation, transmitting side): Inverse S transformation (inverse transformation, receiving side): TS transformation (forward transformation, transmitting side): Inverse TS transformation (inverse transformation, receiving side): where transformation for generating p(n) and the transformation for generating f(n) are respectively called an inverse T transformation and a linear inverse transformation for convenience's sake. As has been described above, the image compressing/expanding device according to this invention is effective and suitable for application to image decoding for a facsimile, a portable information terminal, a display unit and a printer. Patent Citations
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